The Middletons, who were the first to visit their daughter Kate Middleton, Prince William and the new addition, described the baby as "absolutely beautiful", with Carole adding that the new parents were "doing fabulously".
"They're both doing really well," she said of William and Kate, who welcomed their firstborn at 4.24pm on Monday afternoon. "We are so thrilled."
When asked for a clue on the baby's name, she said with a smile, "Absolutely not!"
Carole and Michael arrived at 3pm on Tuesday afternoon, less than 24 hours after their daughter welcomed a little boy.
The delighted couple, who arrived by taxi, smiled excitedly as they made their way inside to see Kate, her husband William, and, of course, enjoy those precious first cuddles with their newborn grandson.
Once Carole and Michael stepped into the private suite where the little Prince was delivered, there would no doubt have been a few tears as the family celebrated this very special moment behind closed doors.
While the arrival of the royal baby is an important historic event, it is of course a tremendous occasion for both the royal family and the Middletons.
The little Prince is not only the first grandchild for Michael and Carole, but also for William's father Prince Charles; a cause for great celebration in both households.
Michael and Carole would have been among the first to receive that joyful phone call from proud new father William on Monday afternoon. While Kate enjoys a famously close relationship with both her parents, William also feels very much at home with the Middleton family and would have taken great delight in sharing the news with them.
Kate's parents arrived in London from their home in Bucklebury, where it is thought the Duchess will spend the first few weeks of motherhood with her baby son.
Carole, in particular, is expected to be instrumental in the little Prince's childhood, and, as such, will play a pivotal role in shaping the future of the monarchy. In the months before the birth, she was pictured shopping with her daughter for the new arrival, and will no doubt been on hand to offer her advice and experience to the couple over the coming months.